Graph 6y+3x=9

Math
6y+3x=9
Solve for y.
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Subtract 3x from both sides of the equation.
6y=9-3x
Divide each term by 6 and simplify.
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Divide each term in 6y=9-3x by 6.
6y6=96+-3×6
Cancel the common factor of 6.
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Cancel the common factor.
6y6=96+-3×6
Divide y by 1.
y=96+-3×6
y=96+-3×6
Simplify each term.
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Cancel the common factor of 9 and 6.
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Factor 3 out of 9.
y=3(3)6+-3×6
Cancel the common factors.
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Factor 3 out of 6.
y=3⋅33⋅2+-3×6
Cancel the common factor.
y=3⋅33⋅2+-3×6
Rewrite the expression.
y=32+-3×6
y=32+-3×6
y=32+-3×6
Cancel the common factor of -3 and 6.
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Factor 3 out of -3x.
y=32+3(-x)6
Cancel the common factors.
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Factor 3 out of 6.
y=32+3(-x)3(2)
Cancel the common factor.
y=32+3(-x)3⋅2
Rewrite the expression.
y=32+-x2
y=32+-x2
y=32+-x2
Move the negative in front of the fraction.
y=32-x2
y=32-x2
y=32-x2
y=32-x2
Rewrite in slope-intercept form.
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The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.
y=mx+b
Reorder 32 and -x2.
y=-x2+32
Rewrite in slope-intercept form.
y=-12x+32
y=-12x+32
Use the slope-intercept form to find the slope and y-intercept.
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Find the values of m and b using the form y=mx+b.
m=-12
b=32
The slope of the line is the value of m, and the y-intercept is the value of b.
Slope: -12
y-intercept: 32
Slope: -12
y-intercept: 32
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.
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Choose 1 to substitute in for x to find the ordered pair.
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Replace the variable x with 1 in the expression.
f(1)=-12+32
Simplify the result.
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Combine the numerators over the common denominator.
f(1)=-1+32
Add -1 and 3.
f(1)=22
Divide 2 by 2.
f(1)=1
The final answer is 1.
1
1
The y value at x=1 is 1.
y=1
y=1
Choose 3 to substitute in for x to find the ordered pair.
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Replace the variable x with 3 in the expression.
f(3)=-32+32
Simplify the result.
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Add -32 and 32.
f(3)=0
The final answer is 0.
0
0
The y value at x=3 is 0.
y=0
y=0
Create a table of the x and y values.
xy1130
xy1130
Graph the line using the slope and the y-intercept, or the points.
Slope: -12
y-intercept: 32
xy1130
Graph 6y+3x=9

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